The Recent Posts and Drafts should be located in the MY DOCUMENTS folder [as you said].
C:\Users\USERNAME\Documents\My Weblog Posts\ OR C:\Documents and Settings\USERSNAME\Documents\My Weblog Posts\
You should be able to double-click them from there, or OPEN WITH [Windows Live Writer] if the file association is broken. All the files in the folder should have a 'WPOST' extension.